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SMALLEST IRREDUCIBLE OF THE FORM x2 ? dy2 1 Introduction - math wisc

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The document discusses the characterization of irreducible polynomials of the form x² - dy² in polynomial rings over finite fields, drawing parallels to classical results regarding primes of the form x² + ny². It presents a theorem that bounds the degree of the smallest irreducible polynomial in this form using an effective version of the Chebotarev density theorem. The paper also explores implications for class field theory and provides conditions under which these bounds hold, ultimately contributing to the understanding of prime ideals in function fields.

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